What is the solution of the equation 5/3−2x=1/6 ?(1 point)

Answer 1

To solve the equation \( \frac{5}{3} - 2x = \frac{1}{6} \), follow these steps:

1. Isolate the term involving \( x \): \[ -2x = \frac{1}{6} - \frac{5}{3} \]

2. Find a common denominator to combine the fractions on the right-hand side: The common denominator for 6 and 3 is 6. Convert \( \frac{5}{3} \) to have a denominator of 6: \[ \frac{5}{3} = \frac{5 \cdot 2}{3 \cdot 2} = \frac{10}{6} \]

3. Now, substitute back into the equation: \[ -2x = \frac{1}{6} - \frac{10}{6} = \frac{1 - 10}{6} = -\frac{9}{6} \] Simplifying \( -\frac{9}{6} \) gives: \[ -\frac{9}{6} = -\frac{3}{2} \]

4. Now, isolate \( x \): \[ -2x = -\frac{3}{2} \]

5. Divide both sides by -2: \[ x = \frac{-\frac{3}{2}}{-2} = \frac{3}{4} \]

The solution to the equation \( \frac{5}{3} - 2x = \frac{1}{6} \) is: \[ \boxed{\frac{3}{4}} \]